This paper proposes a method for vertex-wise flexible sampling of a broad class of graph signals, designed to attain the best possible recovery based on the generalized sampling theory. This is achieved by designing a sampling operator by an optimization problem, which is inherently non-convex, as the best possible recovery imposes a rank constraint. An existing method for vertex-wise flexible sampling is able to control the number of active vertices but cannot incorporate prior knowledge of mandatory or forbidden vertices. To address these challenges, we formulate the operator design as a problem that handles a constraint of the number of active vertices and prior knowledge on specific vertices for sampling, mandatory inclusion or exclusion. We transformed this constrained problem into a difference-of-convex (DC) optimization problem by using the nuclear norm and a DC penalty for vertex selection. To solve this, we develop a convergent solver based on the general double-proximal gradient DC algorithm. The effectiveness of our method is demonstrated through experiments on various graph signal models, including real-world data, showing superior performance in the recovery accuracy by comparing to existing methods.

Manipulation in confined and cluttered environments remains a significant challenge due to partial observability and complex configuration spaces. Effective manipulation in such environments requires an intelligent exploration strategy to safely understand the scene and search the target. In this paper, we propose COMPASS, a multi-stage exploration and manipulation framework featuring a manipulation-aware sampling-based planner. First, we reduce collision risks with a near-field awareness scan to build a local collision map. Additionally, we employ a multi-objective utility function to find viewpoints that are both informative and conducive to subsequent manipulation. Moreover, we perform a constrained manipulation optimization strategy to generate manipulation poses that respect obstacle constraints. To systematically evaluate method's performance under these difficulties, we propose a benchmark of confined-space exploration and manipulation containing four level challenging scenarios. Compared to exploration methods designed for other robots and only considering information gain, our framework increases manipulation success rate by 24.25% in simulations. Real-world experiments demonstrate our method's capability for active sensing and manipulation in confined environments.

This study presents a system integration approach for planning schedules, sequences, tasks, and motions for reconfigurable robots to automatically disassemble constrained structures in a non-destructive manner. Such systems must adapt their configuration and coordination to the target structure, but the large and complex search space makes them prone to local optima. To address this, we integrate multiple robot arms equipped with different types of tools, together with a rotary stage, into a reconfigurable setup. This flexible system is based on a hierarchical optimization method that generates plans meeting multiple preferred conditions under mandatory requirements within a realistic timeframe. The approach employs two many-objective genetic algorithms for sequence and task planning with motion evaluations, followed by constraint programming for scheduling. Because sequence planning has a much larger search space, we introduce a chromosome initialization method tailored to constrained structures to mitigate the risk of local optima. Simulation results demonstrate that the proposed method effectively solves complex problems in reconfigurable robotic disassembly.

Hyperparameter Optimization (HPO) is crucial to develop well-performing machine learning models. In order to ease prototyping and benchmarking of HPO methods, we propose carps, a benchmark framework for Comprehensive Automated Research Performance Studies allowing to evaluate N optimizers on M benchmark tasks. In this first release of carps, we focus on the four most important types of HPO task types: blackbox, multi-fidelity, multi-objective and multi-fidelity-multi-objective. With 3 336 tasks from 5 community benchmark collections and 28 variants of 9 optimizer families, we offer the biggest go-to library to date to evaluate and compare HPO methods. The carps framework relies on a purpose-built, lightweight interface, gluing together optimizers and benchmark tasks. It also features an analysis pipeline, facilitating the evaluation of optimizers on benchmarks. However, navigating a huge number of tasks while developing and comparing methods can be computationally infeasible. To address this, we obtain a subset of representative tasks by minimizing the star discrepancy of the subset, in the space spanned by the full set. As a result, we propose an initial subset of 10 to 30 diverse tasks for each task type, and include functionality to re-compute subsets as more benchmarks become available, enabling efficient evaluations. We also establish a first set of baseline results on these tasks as a measure for future comparisons. With carps (https://www.github.com/automl/CARP-S), we make an important step in the standardization of HPO evaluation.

This allows plugins to solve not only simple toy problems, but also more complex ones, where e.g. an accelerator device is known to behave in an unusual fashion but it is not feasible to fix the issue at the source[29]. Because plugins are independent packages with their own dependency declarations, they can scale from minimal proof-of-concept implementations to complex state machines that call out to subprocesses or request data from the accelerator's monitoring devices. Because plugins have their own versioning scheme, faulty upgrades are trivial to roll back without excessive downtime in the accelerator. The dynamic nature of the plugin architecture also allows plugin developers to test their code using a deployed version of the host application, and include it in a future one. The modular architecture of Geoff also means that plugin developers do not have to use the deployed application at all, and instead e.g.

Prompt optimization is a practical and widely applicable alternative to fine tuning for improving large language model performance. Yet many existing methods evaluate candidate prompts by sampling full outputs, often coupled with self critique or human annotated preferences, which limits scalability, especially for smaller models or models that are not instruction tuned. We present PMPO (Probabilistic Metric Prompt Optimization), a unified framework that uses token level cross entropy as a direct, lightweight evaluation signal. PMPO locates low quality prompt segments via a masking based analysis and iteratively rewrites them to propose improved variants. Crucially, during evaluation, PMPO selects among variants by minimizing loss in a single forward pass, eliminating output sampling and human or judge based scoring for selection while still using standard generation only to propose rewrites. This unified, loss based strategy supports both supervised and preference based tasks. Across model sizes and datasets, PMPO outperforms prior prompt optimizers: it achieves the highest average accuracy on BBH, performs strongly on GSM8K and AQUA RAT, and raises AlpacaEval 2.0 win rates by over 19 points. These results demonstrate PMPO's effectiveness, efficiency, and broad applicability.

This paper introduces the concept of a mean for trajectories and multi-object trajectories (defined as sets or multi-sets of trajectories) along with algorithms for computing them. Specifically, we use the Fréchet mean, and metrics based on the optimal sub-pattern assignment (OSPA) construct, to extend the notion of average from vectors to trajectories and multi-object trajectories. Further, we develop efficient algorithms to compute these means using greedy search and Gibbs sampling. Using distributed multi-object tracking as an application, we demonstrate that the Fréchet mean approach to multi-object trajectory consensus significantly outperforms state-of-the-art distributed multi-object tracking methods.

Distributed optimization requires nodes to coordinate, yet full synchronization scales poorly. When $n$ nodes collaborate through $m$ pairwise regularizers, standard methods demand $\mathcal{O}(m)$ communications per iteration. This paper proposes randomized local coordination: each node independently samples one regularizer uniformly and coordinates only with nodes sharing that term. This exploits partial separability, where each regularizer $G_j$ depends on a subset $S_j \subseteq \{1,\ldots,n\}$ of nodes. For graph-guided regularizers where $|S_j|=2$, expected communication drops to exactly 2 messages per iteration. This method achieves $\tilde{\mathcal{O}}(\varepsilon^{-2})$ iterations for convex objectives and under strong convexity, $\mathcal{O}(\varepsilon^{-1})$ to an $\varepsilon$-solution and $\mathcal{O}(\log(1/\varepsilon))$ to a neighborhood. Replacing the proximal map of the sum $\sum_j G_j$ with the proximal map of a single randomly selected regularizer $G_j$ preserves convergence while eliminating global coordination. Experiments validate both convergence rates and communication efficiency across synthetic and real-world datasets.

A rich vehicle routing problem is considered, allowing multiple trips of heterogeneous vehicles stationed at geographically distributed vehicle depots having access to different modes of transportation. The problem arises from the real-world requirement of optimizing the disaster response time by minimizing the makespan of vehicular routes. Multiple diversely-functional vertices are considered, including Transhipment Ports as inter-modal resource transfer stations. Both simultaneous and split pickup and delivery are considered, for multiple cargo types, along with Vehicle-Cargo and Transhipment Port-Cargo compatibilities. The superiority of the proposed cascaded minimization approach is demonstrated over the existing makespan minimization approaches through our developed Mixed-Integer Linear Programming formulation. To solve the problem quickly for practical implementation in a Disaster Management-specific Decision Support System, an extensive Heuristic Algorithm is devised which utilizes Decision Tree based structuring of possible routes; the Decision Tree approach helps to inherently capture the compatibility issues, while also explore the solution space through stochastic weights. Preferential generation of small route elements is performed, which are integrated into route clusters; we consider multiple different logical integration approaches, as well as shuffling the logics to simultaneously produce multiple independent solutions. Finally, perturbations of the different solutions are done to find better neighbouring solutions. The computational performance of the PSR-GIP Heuristic, on our created novel datasets, indicates that it is able to give good solutions swiftly for practical problems involving large integer instances that the MILP is unable to solve.

Motion planning for robotic manipulators is a fundamental problem in robotics. Classical optimization-based methods typically rely on the gradients of signed distance fields (SDFs) to impose collision-avoidance constraints. However, these methods are susceptible to local minima and may fail when the SDF gradients vanish. Recently, Configuration Space Distance Fields (CDFs) have been introduced, which directly model distances in the robot's configuration space. Unlike workspace SDFs, CDFs are differentiable almost everywhere and thus provide reliable gradient information. On the other hand, gradient-free approaches such as Model Predictive Path Integral (MPPI) control leverage long-horizon rollouts to achieve collision avoidance. While effective, these methods are computationally expensive due to the large number of trajectory samples, repeated collision checks, and the difficulty of designing cost functions with heterogeneous physical units. In this paper, we propose a framework that integrates CDFs with MPPI to enable direct navigation in the robot's configuration space. Leveraging CDF gradients, we unify the MPPI cost in joint-space and reduce the horizon to one step, substantially cutting computation while preserving collision avoidance in practice. We demonstrate that our approach achieves nearly 100% success rates in 2D environments and consistently high success rates in challenging 7-DOF Franka manipulator simulations with complex obstacles. Furthermore, our method attains control frequencies exceeding 750 Hz, substantially outperforming both optimization-based and standard MPPI baselines. These results highlight the effectiveness and efficiency of the proposed CDF-MPPI framework for high-dimensional motion planning.